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A growing number of biological, soft, and active matter systems are observedto exhibit normal diffusive dynamics with a linear growth of the mean squareddisplacement, yet with a non-Gaussian distribution of increments. Based on theChubinsky-Slater idea of a diffusing diffusivity we here establish and analyzea minimal model framework of diffusion processes with fluctuating diffusivity.In particular, we demonstrate the equivalence of the diffusing diffusivityprocess with a superstatistical approach with a distribution of diffusivities,at times shorter than the diffusivity correlation time. At longer times acrossover to a Gaussian distribution with an effective diffusivity emerges.Specifically, we establish a subordination picture of Brownian but non-Gaussiandiffusion processes, that can be used for a wide class of diffusivityfluctuation statistics. Our results are shown to be in excellent agreement withsimulations and numerical evaluations.

Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities